Can anyone help me with this question
Factorize :
13x square-118x+240=0

Dear student,
this can be done using quadratic formula 
$\frac{-b\pm \sqrt{b^2 -4ac}}{2a}$
Given equation : 13x² -118x + 240 = 0
a = 13 , b= -118 , c = 240 

Now b² - 4ac = $(-118{)}^2 - 4\times 13\times 240$
                      = 13924 - 12480 = 1444
x = $\frac{-(-118) \pm \sqrt{1444}}{2\times 13}$
x = $\frac{118 \pm 38}{26}$
x = $\frac{118 +38}{26} or x = \frac{118-38}{26}$
x = $\frac{156}{26} or x = \frac{80}{26}$
x = $\frac{78}{13} or x = \frac{40}{13}$
x = 6 or x= $\frac{40}{13}$
these are the two values of x 

So the factors will be (x - 6 )  and (13x -40)


you can also do this by splitting the middle term. 
Given equation : 13x² -118x + 240 = 0
 Product = a*c = 13*240 = 3120
Sum = -118

two number giving this product and sum are -78 and -40
Now split the middle term as
13x² -78x - 40x + 240 = 0
13x( x - 6 ) -  40(x - 6) 
(x-6)(13x-40) = 0

hence two factors of equation are (x-6 ) and (13x-40)





regards